MATH 554
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Foundations of Topology 2
Mathematics
College of Computational, Mathematical, & Physical Sciences
Course Description
An introduction to the topology of manifolds with particular emphasis on low dimensions: topological and smooth manifolds; smooth maps; tangent spaces; vector fields and flows; Sard's Theorem; Morse Theory; classification of compact manifolds in dimensions 1 and 2; and theory of 3 dimensional manifolds.
When Taught
Winter Even Years
Min
3
Fixed/Max
3
Fixed
3
Fixed
0
Other Prerequisites
Math 553 or instructor's consent
Title
Overview
Learning Outcome
The Fundamental Group
The topology of the plane
Jordan Curve Theorem
Seifert-van Kampen Theorem
Classification of Surfaces
Classification of Covering Spaces
Group Theory
Free groups
Free abelian groups
Presentations of groups
Subgroups of free groups
Title
Learning Outcomes
Learning Outcome
Students should know all relevant definitions, correct statements of the major theorems (including their hypotheses and limitations), and examples and non-examples of the various concepts. The students should be able to demonstrate their mastery by solving non-trivial problems related to these concepts, and by proving simple (but non-trivial) theorems about the concepts below, related to, but not identical to, statements proven by the text or instructor. For more detailed information visit the Math 554 Wiki page.
